(a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. O It is a correct statement. Each interval contains the mean by definition. O It is not a correct statement. Each interval contains the mean by definition. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. I= this statement correct? Why or why not? O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This is the definition of a confidence interval. 14°C
(a) Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval? Explain your reasoning. O The 90% would be wider since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be narrower since the z critical value for 90% is smaller than the z critical value for 95%. O The 90% would be wider since the z critical value for 90% is larger than the z critical value for 95%. O The 90% would be the same since the z critical value for 90% is the same as the z critical value for 95%. (b) Consider the following statement: There is a 95% chance that u is between 7.7 and 9.8. Is this statement correct? Why or why not? O It is not a correct statement. There is a 5% chance that the mean is between these values. O It is a correct statement. There is only a 5% chance that the mean is not between these values. O It is not a correct statement. We are 95% confident in the general procedure for creating the interval, but the mean may or may not be enclosed in this interval. O It is a correct statement. Each interval contains the mean by definition. O It is not a correct statement. Each interval contains the mean by definition. (c) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.7 and 9.8. I= this statement correct? Why or why not? O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for population values. O It is a correct statement. This interval is a great estimate of boundaries for population values. O It is not a correct statement. The interval is an estimate for the sample mean, not a boundary for sample values. O It is not a correct statement. The interval is an estimate for the population mean, not a boundary for population values. O It is a correct statement. This is the definition of a confidence interval. 14°C
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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